Heat Transfer Engineering, 31(6):431–432, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903408268

editorial

Selected Papers From the 19th
National & 8th ISHMT-ASME Heat
and Mass Transfer Conference
SHRIPAD T. REVANKAR1 and SRINATH V. EKKAD2
1
2

School of Nuclear Engineering, Purdue University, West Lafayette, Indiana, USA
Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia, USA

We are glad to present this special issue of Heat Transfer Engineering with a selection of papers presented at the 19th
National & 8th ISHMT-ASME Heat and Mass Transfer Conference, held January 3–5, 2008. The conference was jointly
sponsored by the Indian Society of Heat and Mass Transfer (ISHMT) and the American Society of Mechanical Engineers
(ASME) and was held at the Jawaharlal Nehru Technological University (JNTU), College of Engineering Kukatpally in
Hyderabad, India.

The National Heat and Mass Transfer Conferences (HMTC)
have been held biennially at various places in India since the
inception of ISHMT in 1971. The American Society of Mechanical Engineers (ASME) formally joined the ISHMT in organizing and sponsoring these conferences in 1994. This has
generated greater interaction between researchers from India
and other participating countries. Many well-known experts
from abroad have participated, exchanged technical information, and shared their expertise with Indian researchers through
these conferences and various follow-up workshops and short

courses on topics in heat and mass transfer. At the 19th National
& 8th ISHMT-ASME Heat and Mass Transfer Conference, in
total 330 papers including 2 plenary and 14 keynote papers
were presented. The conference was co-chaired by S. Srinivasa Murthy of Indian Institute of Technology (IIT) Madras
and Srinath V. Ekkad of Virginia Tech, with K. V. Sharma of
JNTU Hyderabad and T. Sundararajan of IIT Madras as conference secretaries. About 500 participants including about 80
from 19 different countries participated in this heat transfer
conference.
Address correspondence to Prof. Shripad T. Revankar, School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907, USA. E-mail:


Here in this special issue eight selected papers covering heat
transfer in turbines, electronic cooling, heat exchangers, refrigeration systems, and materials and efficiencies in power plants
are included. The first paper, “Methods for Conceptual Thermal Design,” presents three models and application methods
that can be used to analyze temperature development in an electronic product during conceptual design. The first model applies
to electronic products used under normal conditions. The second
model calculates hotspot temperature that can be used to evaluate structural concepts during early design stages. The third
model can be used to estimate temperatures in steady-state situations with known boundary conditions obtained from a thermal
mock-up for a functional model. These models are developed
in a resistor–capacitor (RC) network model and can be easily
used as tools for conceptual thermal design. The second paper, “Correlation for Heat Transfer Under Nucleate Boiling on
Horizontal Cylindrical Surface,” presents experimental data on
nucleate boiling heat transfer on horizontal cylindrical heating
elements made out of copper in the medium of Forane around
atmospheric conditions. A heat of boiling/heat transfer correlation is developed based on three nondimensional π groups. The
π groups incorporate the dynamics of bubble growth, dynamics
of flow of the surrounding fluid during the bubble dilatation,
and the influence of the thermal aspects associated with liquid

431



432

S. T. REVANKAR AND S. V. EKKAD

vaporization responsible for the growth of the bubble. The third
paper, “A Parametric Study of an Irreversible Closed Intercooled
Regenerative Brayton Cycle,” presents a thermodynamic analysis of an irreversible regenerated closed Brayton cycle with
variable-temperature heat reservoirs. The optimization is carried out using an entropy generation minimization principle,
and numerical results are presented on the effects of the heat
transfer irreversibility in the hot- and cold-side heat exchangers
and the regenerator, the irreversible compression and expansion
losses in the compressor and turbine, the pressure drop loss at
the heater, cooler, and regenerator as well as in the piping, and
the effect of the finite thermal capacity rate of the heat reservoirs
on the power and efficiency.
The fourth paper, “Conjugate Heat Transfer Analysis in the
Trailing Region of a Gas Turbine Vane,” presents simulation results on the local values of pressure, wall, and fluid temperature,
and area-averaged values of friction factor and Nusselt number
between the smooth and pinned channels and cambered converged channels with and without pin fins, simulating the trailing
region internal cooling passages of a gas turbine vane. The paper highlights interaction between the complex flow pattern and
conjugate heat transfer. The fifth paper, “Experimental Investigation of Cooling Performance of Metal-Based Microchannels,”
presents Al- and Cu-based high-aspect-ratio microchannel heat
exchanger fabrication, and demonstrates through experiment
that the metal-based micro heat exchangers provide improvement in cooling efficiency for microelectronic systems. Given
the energy needs of the world and given coal as the primary
fossil fuel of today, integvrated gasification combined cycle
(IGCC) technology has been identified as an efficient and economic method for generating power from coal with substantially
reduced emissions. The sixth paper, “Numerical Simulation of

Pressure Effects on the Gasification of Australian and Indian
Coals in a Tubular Gasifier,” shows that that the gasification
performance increases for both types of coal when the pressure
is increased.
The seventh paper, “Shell-and-Tube Minichannel Condenser
for Low Refrigerant Charge,” presents a design of a shell-andtube heat pump condenser using 2-mm-ID minichannels with
the expected refrigerant charge less than half the quantity required by a brazed plate condenser giving the same capacity.
Experimental data for heat transfer and pressure drop in this
novel condenser are reported. The last paper, “Experimental Investigation of the Effect of Tube-to-Tube Porous Medium Interconnectors on the Thermohydraulics of Confined Tube Banks,”
presents experiments on the effect of tube-to-tube copper porous
interconnectors on the thermohydraulic performance of an inline and staggered confined tube bank. The data show that a
reduction in the pressure drop by 18% is observed in the inline

heat transfer engineering

configuration, while the heat transfer is enhanced by 100% in
the staggered configuration, when compared to their respective
configurations without the porous medium.
We thank all the authors of these papers for their efforts in
reporting their results, and all the reviewers who have helped
provide timely and informative reviews. We also thank Dr. Afshin Ghajar, editor-in-chief of Heat Transfer Engineering, for
his interest in and support of this special issue.

Shripad T. Revankar is a professor of nuclear engineering and director of the Multiphase and Fuel Cell
Research Laboratory in the School of Nuclear Engineering at Purdue University. He received his B.S.,
M.S., and Ph.D. in physics from Karnatak University,
India, M.Eng. in Nuclear Engineering from McMaster University, Canada, and postdoctoral training at
Lawrence Berkeley Laboratory and at the Nuclear
Engineering Department of the University of California, Berkeley, from 1984 to 1987. His research
interests are in the areas of nuclear reactor thermalhydraulics and safety, multiphase heat transfer, multiphase flow in porous media, instrumentation and

measurement, fuel cell design, simulation and power systems, and nuclear hydrogen generation. He has published more than 200 technical papers in archival
journals and conference proceedings. He is currently chair of the ASME K-13
Committee, executive member of the Transport and Energy Processes Division
of the American Institute of Chemical Engineers, and chair of the Nuclear and
Radiological Division of the American Society for Engineering Education. He
has served as chair of the Thermal Hydraulics Division of the American Nuclear Society. He is on the editorial board of the following four journals: Heat
Transfer Engineering, International Journal of Heat Exchangers, Journal of
Thermodynamics, and ASME Journal of Fuel Cell Science and Technology. He
is a fellow of the ASME.

Srinath V. Ekkad received his B.Tech. degree from
JNTU in Hyderabad, India, and then his M.S. from
Arizona State University and Ph.D. from Texas A&M
University, all in mechanical engineering. He was a
research associate at Texas A&M University and a
senior project engineer at Rolls-Royce, Indianapolis,
before he joined Louisiana State University as an assistant professor in 1998. He moved to Virginia Tech
as an associate professor of mechanical engineering
in Fall 2007. His research is primarily in the area of
heat transfer and fluid mechanics with applications to heat exchangers, gas turbines, and electronic cooling. He has written more than 100 articles in various
journal and proceedings and one book on gas turbine cooling. His research focuses on enhanced heat transfer designs, with a variety of applications. He has
served as coordinator for the 8th ISHMT/ASME Joint Heat and Mass Transfer
Conference held in Hyderabad, India, in January 2008. He was also the chief
organizer for the heat transfer track at the 2004 ASME Turbo Expo. He is also
an associate editor for Journal of Enhanced Heat Transfer and International
Journal of Thermal Sciences. He was the inaugural recipient of the ASME
Bergles–Rohsenow Young Investigator in Heat Transfer Award in 2004 and the
ASME Journal of Heat Transfer Outstanding Reviewer.

vol. 31 no. 6 2010



Heat Transfer Engineering, 31(6):433–448, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903408318

Methods for Conceptual Thermal
Design
RUBEN STRIJK, HAN BREZET, and JORIS VERGEEST
Faculty of Industrial Design Engineering, Delft University of Technology, Delft, The Netherlands

This article describes three generic models and application methods that can be used to analyze temperature development
in an electronic product during conceptual design. The models are based on generally known heat transfer and resistor–
capacitor network theory and are theoretically and numerically approximated. The result is three easy-to-use tools for
conceptual thermal design. Application of the models in design practice has been assessed using a usability experiment and
several in-depth interviews with industrial design engineers from the field.

INTRODUCTION
The latest changes in industry require companies to focus
on fast innovations. The result is that time to market is shortened and development speed is increased [1]. Therefore, we
have less time to develop products that are reliable and have
good quality. In addition, the amount of electronics around us
is increasing, ubiquitous electronics [2], and the power density
is increasing by continuous miniaturization. The result is that
reliability becomes an increasing important issue in development of electronic products [3] and thermal design becomes a
bottleneck in the development process. It is therefore necessary
to provide electronic and mechanical engineers with tools and
methods to take temperature into account in preliminary phases
in design.

Some research has been done to improve thermal analysis in
the conceptual phases. Ishizuka and Hayama [4], for instance,
describe models to simplify analysis of natural convective cooling in preliminary analysis. Yazawa and Bar-Cohen’s studies on
flow models [5] also contribute to this issue. However, in our
best knowledge there are no generic models available that can
be used in conceptual design of electronic systems. Our goal is
to extend the present knowledge on resistor–capacitor networks
(RC networks) and flow modeling to develop generic models
for application in conceptual thermal design.
During our preliminary studies several designers from practice have been interviewed with the aim of verifying the application of thermal management techniques in practice. Different
Address correspondence to Professor Ruben Strijk, Faculty of Industrial
Design Engineering, Delft University of Technology, Landbergstraat 15, 2628
CE Delft, The Netherlands. E-mail:

views indicate how practicing designers work in the field of
thermal design. Three key issues derived from interviews and
literature are:
1. Designers are unfamiliar with heat transfer and thermal design theories. Such designers lack the knowledge that would
enable them to make basic design choices and evaluate how
important temperature is to the design. The choice between
passive and active cooling is currently based on experience
and trial and error.
2. An evaluation of structural concepts on temperature development is not supported by a standard approach.
3. Temperature measurements for mock-ups and functional
models are crucial in thermal design practice for finding
reliable boundary conditions, but are time-consuming. The
process of measuring could possibly be optimized by properly integrating easy-to-use formulas that could be calibrated
using measurements determined from a thermal mock-up or
functional model. The effects of design changes could be
predicted by predefined rules of experience and estimations.

Furthermore, as has been concluded from studying the literature and has been clearly expressed by participants during
interviews, any tool used for conceptual design should be easy
to use. To resolve the three issues just listed, three models have
been developed that contain the following three characteristics:
Model 1 supports risk assessments put forth by the designer,
even if he or she has no knowledge of heat transfer or thermal
design [6–8]. Model 2 supports finding and analyzing the main
heat path in structural concepts and is useful for estimating
rough temperatures in an electronic product [8–10]. Model 3

433


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R. STRIJK ET AL.

supports the determination of the total transient behavior in a
device [8, 11]. The contribution of this article is the proposal
and evaluation of these three models and application methods.

APPROACH
This article is constructed of several sections to propose and
evaluate the three models. In the approach for model 1, basic
heat transfer calculations are combined with measurements for
existing products. Heat transfer calculations show maximum
boundary conditions of heat transfer for a surface area. This
is done using several surface temperature differences within
the environment. Measurements combined with these values
show a transition area that can be used as a guideline for a

particular design. For model 2, an RC network is developed
and programmed into a small software program. The industrial
designer can use this program to fill in variables and calculate
temperatures. Finally, model 3 describes a mathematical model
for temperature prediction in an electronic product. As a basis for
the model, an electronic product will be viewed as if it were one
single hotspot within an encasing. In reality, the hotspot could be
a power-dissipating component, such as a coil, integrated circuit
(IC), or the average temperature of a printed circuit board. The
model can be used to describe the effect of design changes on
hotspot temperature. Several design variables will be taken into
account, including an open or closed encasing, passive cooling
or active cooling, and materials used for the encasing. In this
article, four steps that define the models will be listed: model
description, results and discussion, practical application, and
conclusion.
Step 1: Model description. Describing the three proposed models based on general heat transfer theory and thermal
RC networks.
Step 2: Results and discussion. The application of the three
models will be described for example situations and
real products. The heat transfer variables that are
needed in the equations are derived from standard conduction, convection, and radiation equations. The section follows with a description of the results of the
measurements. The differences between the measured
and calculated values are discussed and directions for
improving the accuracy of the model are given.
Step 3: Practical application. The practical use of the models
in a design situation is described.
Step 4: Conclusion. Drawing conclusions from the research in
described in this article.


limits for an electronic product is explained. The theoretical
cooling limit is derived by combining convective and radiative
heat transfer coefficients from an isothermal surface to an ambient environment. As a basis for model 2, an electronic product
is examined as one single hotspot within an encasing. In reality,
the hotspot can include a power dissipating component, such as
a coil, an integrated circuit (IC), or the components of a printed
circuit board (PCB). Model 3 is a framework for evaluating
various cooling concepts and is based on an RC network. The
objective of the model is to give insight into transient behaviors
of the hotspot and encasing temperatures for different cooling
configurations.
Model 1
Passive cooling limits have been calculated for the temperature differences between a hot surface with an ambient environment. By comparing these values with measurements for
existing products, boundary areas for the passive and active
cooling of an electronic product and a maximum power-to-area
ratio for electronic products can be defined. These calculations
are for heat transfers between an isothermal surface temperature Te and the ambient temperature Ta = 296 K (= 23◦ C). A
specific dimension for a vertical plate Lc of 0.1m and thermal
conductivity of air kair is used to calculate the heat transfer coefficient for convection hc and the heat transfer coefficient for
radiation hr at temperature differences T (= Te − Ta ) of 5 K,
15 K and 25 K, shown in Table 1.
The heat transfer coefficients hc and hr have been approximated based on general heat transfer theory for a vertical plate
with an isothermal temperature distribution across the surface.
To determine hc , the Hilpert correlation, shown in Eq. (1), has
been used to approximate the Nusselt number Nu [12].
kair NuL
[W/m2 K]; Nusselt, NuL = 0.54RaL0.25
(1)
L
The heat transfer coefficient of radiation hr is determined by

using the average temperature Tav , and is shown in Eq. (2). Here,
qr is the radiation heat transfer [W], ε is the emissivity of the
radiating surface [1.0], σ is the Stefan–Boltzmann constant [5.67
× 10−8 ], F1,2 is the radiation shape factor, A is the radiation
surface area, T1 is the surface temperature of object 1, T2 is the
surface temperature of object 2, and Tav is the average surface
temperature between object 1 and object 2.
hc =

3
hr = εσF1,2 4Tav
[W/m2 K]

Table 1 Natural convection and radiation heat transfer coefficients for three
temperature differences, calculated using Eq. (1) and Eq. (2) for an ambient
temperature Ta = 296 K
h [W/(m2 K)]

MODEL DESCRIPTION
In this section a description of the proposed models is given.
For model 1 the theoretical approximation of passive cooling
heat transfer engineering

(2)

T=5K
6.0
3.7
9.7


hr
hc
htot

vol. 31 no. 6 2010

T = 15 K
6.3
4.9
11.2

T = 25 K
6.7
5.5
12.2


R. STRIJK ET AL.

The resulting total heat transfer coefficient htot , given in
Eq. (3), is then calculated by summing hc and hr . The temperature difference of 15 K is comparable with previous studies found in literature [5]. The temperature differences of 5 K
and 25 K define a transition area between passive and active
cooling.
htot = hr + hc

(3)

Table 1 gives results for the three temperature differences
just described. The results show that, for the given Ta , hc is
significantly dependent on temperature differences between the

surface and the environment, while hr is not. In addition, it can
be concluded that in passive cooling, radiation heat transfer can
play a significant role because it is in the same order of magnitude as convection heat transfer. However, this only accounts
for black- and gray-body radiation, where ε ≈ 1.0.
Model 2
As a basis for model 2 and model 3, this article examines an
electronic product as one single hotspot within an encasing. In
reality, the hotspot can include a power dissipating component,
such as a coil, an integrated circuit (IC), or the components of a
printed circuit board (PCB). Based on this abstraction, various
models can be derived, ranging from a very simple RC network,
which is discussed in this section, to a complex RC network.
In this section, mathematical relations of the one-dimensional
heat transfer will be derived. This is done by proposing a onedimensional RC network, given in Figure 1, that can be applied
to a variety of electronic products that are passively cooled and
have a closed encasing. Based on insights gained through this
analysis, the mathematical model may be expanded into something more complex. This will be explored in future research if
required.
When designing electronic products, it can be important to
predict the behavior of a product within a certain period of time.
For this particular model, it is necessary to take into account
transient temperature development. By using transient temperature prediction in the form of state space equations, the model
allows for the option of evaluating a usage scenario. This usage scenario can then be evaluated and compared with defined
criteria. Based on such results, the product can be properly
designed without overdimensioning, which would bring about
higher costs.

Figure 1 Thermal RC network model 2.

heat transfer engineering


435

The system consists of five types of variables: thermal resistors R, temperature T , thermal capacitors C, heat flow q, and
energy E. Four thermal resistors include the following:
•

The core of the hotspot to the surface of the hotspot, or R1 .
The hotspot surface to the interior surface of the encasing, or
R2 .
• The interior surface of the encasing to the exterior surface of
the encasing, or R3 .
• The exterior surface of the encasing to the ambient environment, or R4 .
•

The temperatures in the product result from the hotspot heat
flow q and the thermal resistors, q = R T. In this model, five
temperatures are defined:
•
•
•

The temperature inside the hotspot, or Tc .
The temperature of the hotspot surface, or Th .
The temperature of the interior surface of the encasing, or Ti .
• The temperature of the exterior surface of the encasing, or Te .
• The ambient temperature, or Ta .
In order to calculate transient temperature development, thermal capacity must be taken into account. Generally, electronic
products consist of an encasing on the outside and electronics
on the inside. Between the electronics and the encasing, there is

generally air. Usually, this means that when a product is heated,
there are three thermal capacitors (Figure 1) that cause temperatures to rise at a steady rate:
•
•
•

The thermal capacitance of the hotspot, or C1 .
The thermal capacitance of the inside air, or C2 .
The thermal capacitance of the encasing, or C3 .

The main heat flow in the system q causes temperatures
to rise. Three heat flow paths into thermal capacitances result
from this general heat flow. The heat flow paths into these three
thermal capacitances are defined as follows:
•
•
•

Heat flow into C1 , or q1 .
Heat flow into C2 , or q2 .
Heat flow into C3 , or q3 .

The heat flow in the model will result in four basic temperature differences:
•

From the core of the hotspot to the surface of the hotspot, or
Tc − Th .
• From hotspot surface to the interior of the encasing, or Th −Ti .
• From the interior of the encasing to the exterior of the encasing, or Ti − Te .
• From the exterior of the encasing to the ambient environment,

or Te − Ta .
By combining these temperature differences, other temperature differences can be derived, for example, the temperature
difference between a hotspot surface and exterior encasing,
Th − Te , equals (Th − Ti ) + (Ti − Te ). For practical reasons,
vol. 31 no. 6 2010


436

R. STRIJK ET AL.

only the temperatures Th , Te and Ta will be measured and compared, with resulting temperature differences of Th −Te , Te −Ta ,
and Th − Ta .
Finally, the total energy stored in the capacitances in the
system can be defined by the product of thermal capacitance
and temperature, or E = CT. However, in the present case, of
greatest interest are temperature differences with regard to a
reference temperature Ta . Therefore, the energy stored in the
system is defined as reference energies Eref 1 = C1 Ta , Eref 2 =
C2 Ta and Eref 3 = C3 Ta for the following thermal capacitances:
Energy stored in C1 , or E1 = C1 Tc − Eref 1 → E1 = C1 (Tc −
Ta ).
• Energy stored in C2 , or E2 = C2 Th − Eref 2 → E2 = C2 (Th −
Ta ).
• Energy stored in C3 , or E3 = C3 Ti − Eref 3 → E3 = C3 (Ti −
Ta ).
•

State space equations allow for the possibility of dynamically
analyzing temperatures. A designer may use the equations to

calculate temperature from any realistic starting condition. For
instance, the model can be integrated and computed into a software program in which the designer fulfills required parameters
and usage scenarios. The program then calculates temperature
development in the device. This section describes these state
space equations and their parameters. State space equations
basically consist of two equations. The first equation defines
˙
air flow into thermal capacitances, X(t)
= AX(t) + BU (t).
The second equation is used to examine temperature differences Y (t) = CX(t) + DU (t). The matrices are defined as
follows [13]:
•
•
•

•
•
•
•
•

˙
X(t)
are the heat flows into thermal capacitances.
A is the system matrix and contains the values of thermal
resistances and capacitances.
X(t) is the vector describing the state of the system, which is
the energy stored in thermal capacitances with regards to the
reference temperature Ta .
U (t) is the input vector and describes the quantity of heat that

flows from the hotspot into the system.
B is the control matrix.
Y (t) is the output of the system.
C is the output matrix of the system.
D is the feed-forward matrix.

State space equations based on this system can be defined as
follows:
⎛
⎞
⎛ ⎞
C1 Tc − Eref 1
q1
˙
X(t) = ⎝ C2 Th − Eref 2 ⎠ ; X(t)
= ⎝ q2 ⎠ ;
C3 Ti − Eref 3
q3
⎞
T c − Th
⎜ T h − Ti ⎟
⎟
U (t) = q; Y (t) = ⎜
⎝ T i − Te ⎠
Ta − Te

⎧
⎛
1
1

⎪
⎪
−
⎪
⎪
⎜
C
R
C
R1
⎪
1
1
2
⎪
⎜
⎪
⎪
⎜ 1
⎪
1
1
⎪
˙
⎪
−
−
X(t)
=⎜
⎪

⎜ C1 R1
⎪
C2 R 1
C2 R2
⎪
⎜
⎪
⎪
⎝
⎪
⎪
1
⎪
⎪
0
⎪
⎪
C
R2
⎪
2
⎪
⎪
⎛ ⎞
⎪
⎪
⎪
1
⎪
⎪

⎪
⎜ ⎟
⎪
⎨
+ ⎝ 0 ⎠ U (t)
0
⎪
⎪
⎪
⎪
⎛
⎪
⎪
1
1
⎪
⎪
−
⎪
⎪
⎜ C1
C2
⎪
⎪
⎜
⎪
⎪
⎜
1
⎪

⎪
⎜0
⎪
⎪
⎜
⎪
C2
⎪
⎜
Y (t) = ⎜
⎪
⎪
⎪
⎪
⎜0
⎪
0
⎪
⎜
⎪
⎪
⎜
⎪
⎪
⎝
⎪
⎪
⎩
0
0


⎞
0
1
C3 R2
−

1
1
−
C3 R2
C3 (R3 + R4 )

(4)
⎞

0

⎟
⎛ ⎞
⎟
0
⎟
1
⎟
⎜ ⎟
−
⎟
⎜0⎟
C3

⎟ X(t) + ⎜ ⎟ U (t)
⎟
⎜0⎟
R3
⎟
⎝ ⎠
C3 (R3 + R4 ) ⎟
⎟
0
⎠
R4
C3 (R3 + R4 )

Model 3
In this section, a framework for evaluating various cooling
concepts is described. The framework is based on an RC network, shown in Figure 2. The objective of the model is to give
insight into transient behaviors of the hotspot and encasing temperatures.
In the thermal RC network, there are several heat flows that
must be taken into account. The source for the heat flow is
q. As a result of q, the product begins to heat. This property is
represented by heat q1 into thermal capacitance C. As a result of
the heat flow in C, the temperature of the product rises and heat
flows to an ambient environment. The heat flow to the ambient
environment can be divided in two flows. First, a possible forced
or passively induced flow of air through the device via openings
in the encasing may exist. This is represented by q2 . Second,
a flow of heat in the form of natural convection and radiation
through the encasing q3 may also be present.
There are several thermal resistances that determine power
flows and temperature distribution within a system. First, a thermal resistance models heat transfer through a flow of air through

the product R1 . This can occur through either natural or forced
convection. For fully closed encasings, the value of this thermal
resistance will be set to infinite ∞. Second, the model contains
two thermal resistances that describe the heat flow q3 through
the encasing. This includes heat flow from the hotspot to the
exterior of the encasing R2 and heat flow from the exterior of

⎛

heat transfer engineering

⎟
⎟
⎟
⎟ X(t)
⎟
⎟
⎠

Figure 2 Thermal RC-network model 3.

vol. 31 no. 6 2010


R. STRIJK ET AL.

437

the encasing to an ambient environment R3 . The result of these
described thermal resistances and heat flows of a product within

a specific ambient temperature Ta is a hotspot temperature of Th
and an average encasing exterior temperature of Te . Integration
of the previous equation results in the following equation:
−t

T (t) = Tm − e( RC ) (Tm − Ta )

(5)

From Eq. (5) two equations can be derived given by Eq. (6):
⎡ R (R + R ) R (R + R ) ⎤
1

Th (t)
Te (t)

=

Ta
Ta

2

3

1

2

3


⎢ R1 + R2 + R3 R1 + R2 + R3 ⎥
⎥
+⎢
⎣
⎦
R1 R3
R1 R 3
R1 + R2 + R3 R1 + R2 + R3

×

q
−t
−qe( RC )

(6)

For a closed encasing, the value of R1 can be defined as
infinite, resulting in Eq. (7):
Th (t)
Te (t)

=

Ta
Ta

+


R2 + R3 R2 + R3
R3
R3

q
−t
−qe( RC )

(7)

RESULTS AND DISCUSSION
In this section the results and discussion of the three models
are presented and described. A more extensive elaboration of
the results has been described in previous publications [7, 8, 10,
11].

Model 1
The surface area A and power dissipation q have been measured for a 66-product total. Figure 3 shows both the calculated
heat transfer lines (Table 1) and the positioning of the experimental results. The values of A varied between 8.0 × 10−3 m2
(portable radio) and 3.0 m2 (washing machine), while q varied
between 2.0 × 10−2 W (portable radio) and 2.0 × 103 W (water
cooker). Figure 3 shows that most products that dissipate less
than 1 W of power are positioned below the 5 K temperature
line. Product examples in this range include a Discman, radio,
MP3 player, and minidisk. It is probable that thermal design
was not a major issue in the development of these products.
Examples of products that are positioned around the 5 K line
up to the 15 K line include stereos, cathode ray tube TVs, LCD
(liquid crystal display) TVs, network switches, and routers. It
would be likely that thermal design played a significant role in

the design process of these products. For instance, an LCD TV
uses holes in the encasing, combined with a significant amount
of cooling fins on the inside of the product, to dissipate heat
from the printed circuit board to an ambient environment.
heat transfer engineering

Figure 3 Existing products and theoretical cooling limits, based on own measurements.

In the “actively cooled” range, between the 15 K and 25 K
lines, products such as a laptop computer are positioned. These
types of products are generally regarded as in critical need of
proper thermal design. In the area above 25 K, products such
as power tools, kitchen appliances, and slide projectors can be
found. Power tools that use an electromotor usually have a relatively short duty cycle and therefore generally do not reach
their steady-state temperature. Products that are convectively
cooled are cooled by airflow induced by a rotating component,
sometimes a fan directly connected to the electromotor. Other
products in this range, such as kitchen appliances and slide
projectors, generally give off a great deal of heat. Thermal design is very critical in these types of products. Temperatures of
hotspots in these types of products are usually much higher than
in products within the range of 15 K to 25 K.

Model 2
In order to investigate the accuracy of state space equations
and the assumptions made in the previous section, computations
will be based on the properties of an actual product, in this case,
a standard AC–DC adaptor shown in Figure 4. Comparisons of
the measurements with the model will give conclusions about
the accuracy and applicability of the model for design engineering purposes. The measurements have been executed using
thermocouples and an infrared sensor. Data has been collected

by means of a data logger, which measures and stores the temperatures of the hotspot Th , the encasing Te , and the ambient
temperature Ta .
For the purposes of this comparison, both measurements and
computations have been subjected to two different degrees of
power dissipation, including 1 W and 2 W. The aim is to gain
insight into the extent to which the model can predict variations in temperatures, depending on the different amounts of
vol. 31 no. 6 2010


438

R. STRIJK ET AL.

Figure 4 Overview of an AC-DC adaptor.

dissipated power. The heat transfer coefficients for convection
and radiation are influenced by factors such as temperature differences and geometry. In this model, a combined heat transfer
coefficient for convection and radiation is used. Equation (1)
has been used to approximate the Nusselt number, Nu. The
heat transfer coefficient of radiation is approximated by using
Eq. (2). State space equations have been programmed using a
C++ script in order to determine their solutions. The script is
an algorithm based on the explicit Euler method for calculating differential equations. The script can be used to develop
a software program from which a practical application can be
tested.
The results of the computed model and measured product
are shown in Figures 5 to 7. Two initial tests on the adaptor
have been carried out and include 1-W and 2-W heat dissipation. Table 2 shows the results of the model and measurements.
The first approximation results in steady-state temperatures that
significantly deviate from the measurements. Th − Te has been

computed using a factor of 2.46 (12.78/5.20), which is too high.
Te − Ta has been computed using a factor of 0.48 (5.80/12.20),
which is too low.
In addition, infrared measurements have been carried out on
the adaptor for steady-state temperatures shown in Figure 8.

Figure 5 Measured and computed temperatures for 1W dissipation.

heat transfer engineering

Figure 6 Measured and computed temperatures for 2W dissipation.

The approximate location of the hotspot is also shown in this
figure. The results illustrate that temperatures across the encasing surface are not constant, but vary from 38.0◦ C (= 311
K) to 24.5◦ C (= 297.5 K). The average of these two values is
31.3◦ C (= 304.3 K). From the figure, it can be determined that
high temperature concentrations are found at the approximate
location of the hotspot.
From the data in Table 2, several conclusions can be drawn.
We can see that t98% can be estimated within an accuracy of 17%.
t98% , computed with the model, appears to be a relatively good
approximation with regard to the measured t98% . In addition, the
model predicts the effects of temperature changes by observing
changes in the concept, in this case, a change in power dissipation. The present results show that although measured and
computed temperatures do not correspond, the temperatures of
the computations do proportionally change with measured temperatures when dissipated power is changed from 1 W to 2 W.
This is a positive effect, which shows that the model accurately

Figure 7 Measured and computed temperatures for improved model results
for 1W dissipation.


vol. 31 no. 6 2010


R. STRIJK ET AL.
Table 2 Measurement and computation results

Variable
R1 [K/W]
R2 [K/W]
R3 [K/W]
R4 [K/W]
C1 [J/K]
C2 [J/K]
C3 [J/K]
t98% [s]
Ti − Th [K]
Th − Te [K]
Te − Ta [K]
Th − Ta [K]

1-W
2-W
1-W 2-W
1-W
measurement measurement model model improved model
—
5.20
—
12.20

—
—
—
3840
—
5.20
12.20
17.40

—
5.20
—
12.20
—
—
—
5280
—
10.50
22.60
33.1

0.20
12.00
0.79
5.81
47.91
0.08
64.00
4500

0.20
12.78
5.80
18.58

0.20
12.00
0.79
5.81
47.91
0.08
64.00
4500
0.40
25.56
11.61
37.17

0.20
7.19
0.79
5.81
47.91
0.08
64.00
3800
0.20
7.98
5.81
13.63


439

It is unlikely that the dissipated power q, the measured temperature Th , or the surface area Ah encompasses this problem
because these values were controlled during the test setup. A
different explanation is that the thermal resistance R2 has been
incorrectly approximated. Because the air layer between the
hotspot and inside encasing is relatively thin, on average, measuring 2.5 mm, the conductive heat transfer through the inside
air should be taken into account. If done, the following improvement will result:
L=

= 2.5 mm
hk =

predicts the effect of power changes on temperatures for a particular concept.
However, the results also show that temperature differences
from a hotspot to the encasing and from the encasing to an
ambient environment are incorrectly computed (Figures 5 and
6). First, the measured Th − Te and Te − Ta values (in Figures 5,
6, and 7 these are squares and dots, respectively) deviate a
great deal from computed values. However, the sum of the two
computed and measured values of Th − Te and Te − Ta , namely,
Th − Ta , does not deviate a great deal. We can see that the model
predicts the hotspot temperature with an accuracy of 8% to
21%.
The problem with the model is that the wrong computations for Ti − Th and Te − Ta are given. The cause of this
miscalculation is an incorrect estimation of thermal resistances
R2 and R4 . R2 has been computed too high, with a factor of
2.46 (12.78/5.20), resulting in a high estimation of Th − Te . R4
has been computed too low, with a factor of 0.48 (5.80/12.20),

resulting in a low estimation of Te − Ta (Table 2). The remainder of this section discusses the probable causes of both
problems.

Figure 8 Steady-state temperatures of the adaptor.

heat transfer engineering

44 − 35 − 4
We − Wh − 2 × thickness
=
2
2

kair
24.0 × 10−3
⇒ hk =
= 9.6 W/m2 K
L
2.5 × 10−3

Th − Ti = qR2 =
=

q
(hc + hr + hk )Ah

1
= 7.2 K
(6.9 + 6.7 + 9.6)0.6 × 10−2


These calculations include the heat transfer coefficient of
conduction, hk , with the inside air results in T of 7.98 K.
This comes far closer to the measured temperature difference
of (5.20 K), compared to 12.78 K, derived from previous calculations. Therefore, for this product, air conduction inside the
product plays a significant role in determining the temperature difference between the encasing and the hotspot when air
layers are 2.5 mm. Further exploration is advised and should
take into account more details of the hotspot and the encasing when calculating heat transfer coefficients and thermal
resistance.
As can be seen in Figure 8, the temperature is not evenly distributed across the surface of the encasing. A temperature difference T of 13.5 K between the lowest and highest temperatures
is measured. If the T between the maximum temperature and
the average temperature is calculated, the following results are
reached: 38.0◦ C – 31.25◦ C = 6.75◦ C = 6.75 K. It is likely
that because only one thermocouple was used, a higher than
average temperature was measured on one hand, while the average temperature was calculated on the other. The differences
between measured and calculated temperatures are 12.20◦ C –
5.80◦ C = 6.40◦ C = 6.40 K, which comes close to T between
the maximum and average temperatures. In the previous section
it was concluded that R4 is computed with a too low factor of
0.48 resulting in a low estimation of the temperature difference
Te − Ta . One option for correcting this factor includes increasing the total heat transfer coefficient. This, however, would be
a very unrealistic assumption. It is unlikely that the convection
and radiation heat transfer coefficients, hc in Eq. (1) and hr in
Eq. (2), have been estimated low. The heat transfer coefficient
for convection has been estimated using a correlation for the
Nusselt number of a vertical plate [12]. This correlation already
vol. 31 no. 6 2010


440


R. STRIJK ET AL.

results in a relatively high convection coefficient. In addition,
the radiation heat transfer coefficient also has been calculated
relatively high because a maximum emissivity ε = 1 and maximum view factor F1,2 = 1 have been used. The previous section
discussed how conduction plays a significant role in calculating
R2 because of a thin air layer between the hotspot surface and the
inside encasing surface. It is unlikely that this has a significant
influence over the calculation of R4 , since the air on the outside
of the product can move freely from the encasing surface to an
ambient environment. A comprehensive elaboration is given in
Teerstra’s article on natural convection in electronic enclosures
[14].
Assuming that heat dissipation q and the area of heat transfer
Ah have been correctly controlled in measurement calculations,
the only option remaining is the deviation of temperatures on the
encasing surface with regard to the average temperature, which
is also calculated using the proposed model. Infrared measurements (Figure 8) indicate that temperatures of the encasing are
difficult to predict in detail. The difference between computations and measurements, 12.2 K – 5.8 K = 6.4 K, is of the same
magnitude as differences measured, 6.75 K. The model thus predicts the average temperature of the encasing, but cannot predict
local temperatures.
The parameter t98% does not vary between various levels of
power dissipation in the model. The temperature development
in the model is exactly the same for both rates of dissipation,
1 W and 2 W, namely 4500 s. However, measurements indicate that, in reality, there is a significant difference between the
measured value of t98% (1 W: 3840 s and 2 W: 5280 s). This
does not appear to be a result from a miscalculation of thermal
capacitances C1 , C2 , and C3 because it is a straightforward calculation. Therefore, it can be concluded that the proposed model
does not take into account the effect of temperature on transient
temperature prediction. This issue should be taken into account

when undergoing follow-up research.

Model 3
In this section, the results of the thermocouple measurements are presented. There are several reasons for obtaining the
present measurements. First, the measurements are needed to
obtain more insight into heat transfer and the distribution of
temperature within a mock-up. Second, measurements give insight into differences for possible cooling configurations. Third,
the measurements will be used at the end of this chapter to
compare predictions with a calibrated model and evaluate the
predictability and accuracy of the model.
Because the intention is to obtain insight into the effects of
design changes, these measurements will cover different configurations given in Figure 9. A mock-up is a device that contains
one hotspot, in this case, a piece of copper with a resistor inside.
Many of these design options can be varied, as is shown in the
following:
heat transfer engineering

Figure 9 Several mock-up configurations.
•

The encasing material can be changed (polystyrene and aluminum).
• The encasing can be either closed or open.
• The airflow can be changed from natural convection to forced
convection by integrating a small fan.
• The surface area of the hotspot can be increased (cooling fins).
The temperature of each setup has been measured by means
of a data logger. All temperatures are logged once each minute
until a steady-state situation has been reached. Temperature
measurements have been achieved within a laboratory environment, using an ambient temperature Ta that varied by ±2 K
around an ambient temperature of approximately 296 K (=

23◦ C). The fluctuations in ambient temperature fall within a
reasonable range. To interpret the data, temperature differences
are used. This is a convenient method for correcting fluctuations in ambient temperature. T-type thermocouples have been
attached to the hotspot and the top, bottom, front, back, left
and right of the encasing. The reference temperature has been
attached to the tripod that holds the mock-up. Figure 10 gives an
overview of the measurement set-up and the components used
to build the different configurations.
Each configuration has been tested for at least three different
ranges of power dissipation. The ranges were chosen in such a
way that the level of maximum power delivers a hotspot temperature between 333 K (= 60◦ C) and 343 K (= 70◦ C). This
temperature limit results from achieving the maximum allowed
temperature for the material used in the mock-up (polystyrene).
In total, 38 measurements have been executed. The aim of the
present study is to discuss the predictability of Eqs. (5)–(7). The
average encasing temperature is derived from measurements
taken from the top, bottom, front, back, left, and right of the
encasing.
For configuration A, Th is higher with aluminum than with
polystyrene. For all other configurations, however, this is not the
case. It could be suggested that in the case of configuration A,
the emissivity of the encasing material plays a significant role.
The emissivity of white plastic is between 0.84 and 0.95 [15] and
vol. 31 no. 6 2010


R. STRIJK ET AL.

Figure 10 Overview of the set-up for thermocouple mock-up measurement.


the emissivity of polished aluminum is between 0.04 and 0.06
[16], which should result in a large difference in heat transfer
coefficients between the two materials. Radiation is a complex
phenomenon. It would not be appropriate to conclude more
than the preceding suggestions based solely on thermocouple
measurements. Figure 11 shows that for the thermal mock-up
presented here, the encasing material influences hotspot temperature. Implementing an encasing material with a high level
of conductivity (aluminum) will result in lower hotspot temperatures, because heat can spread more easily throughout the
material. This effect is highly noticed in the case of configuration E, where the hotspot is attached to the encasing. For a
power dissipation of 1.0 W, the T of aluminum is 50% of the
T of polystyrene.
Comparing configuration C with configuration B in Figure 11
leads to the suggestion that, for open encasings, extending the
cooling surface by means of cooling fins results in a lower
hotspot temperature. Figure 12 shows, however, that this is
not necessarily the case for an average encasing temperature.

Figure 11 and Figure 12 suggest that a ventilated product, by
means of forced convection, significantly reduces both Th and
Te . For configuration F, which is unvented but uses forced convection inside, an approximate 50% reduction in hotspot temperature, with regard to configuration A and B, is observed.
In most cases, thermal resistance is higher at low power dissipations. This suggests that the effect is related to nonlinear
behavior of the heat transfer coefficient. For configurations A,
B, C, D, and F, the effects of changing encasing materials are
relatively small. Configuration E (the hotspot is attached to
the encasing) indicates a significant difference between using
polystyrene and aluminum as an encasing material. For both
cases presented in configuration C, a clear reduction in hotspot
temperature by enlarging the cooling surface (cooling fins) is
realized. In general, the hotspot temperature is lower when an
aluminum encasing is used, and by adding a fan, the setup could

dissipate a significantly higher amount of power, resulting in
a factor of approximately seven times the power dissipation,
compared to the average hotspot temperature. With configuration E, the effects on hotspot temperature are very large in both
cases, with a 30% to 70% improvement. Configuration F shows
that internal air circulation can reduce hotspot temperature by
approximately 50%, compared to configuration A.
For configurations A and F, there is generally little difference between maximum encasing and average encasing temperatures. Configurations C, D, and E show a large difference
between maximum encasing temperature and average encasing temperature. There is a noticeably large difference between
aluminum and polystyrene. Aluminum, with its higher thermal
conductivity, better distributes heat and reduces differences between average and maximum encasing temperatures. By far,
configuration E gives the highest rate between maximum and
average encasing temperatures, which is likely due to the fact
that the hotspot has been attached to the encasing.
Time constants derived using a function for unconstrained
minimization algorithm in Matlab are presented in Table 3. Time
constants derived using data from temperature measurements for
the hotspot appear relatively consistent per configuration. One
that significantly differs is Al E-0.25. This deviation is a result of
high fluctuations in temperature measurements during startup.

Figure 11 Temperature differences from the hotspot to an ambient environment.

heat transfer engineering

441

vol. 31 no. 6 2010


442


R. STRIJK ET AL.

Figure 12 Temperature differences for the average encasing to an ambient environment.

The total thermal resistance and capacitance of Eq. (5) can be
derived from measurements.
The derived results of the thermal resistance and capacitance
for the 12 different configurations are displayed in Table 4 and
Table 5. Thermal resistance values and capacitance appear to
be relatively consistent per configuration. Thermal resistance
significantly decreases in configuration D, where a fan was
used. The large difference between thermal resistance values
for polystyrene configuration E and aluminum configuration E
explains the positive effect of heat spread by using a material
with high levels of thermal conductivity, compared to a material
with low levels of thermal conductivity. Configurations A and
B have approximately the same thermal capacitance. However,
the amount in configuration B is slightly less because some
material has been removed from the top and bottom of the encasing. In configuration C, cooling fins have been added. These
are made of aluminum and therefore result in a higher level of
thermal capacitance. In configuration D, a small fan has been
added in addition to the cooling fins. This, again, results in an
increase of thermal capacitance. Configuration E has one value
for the aluminum encasing that is significantly different from
the other values. This is most likely caused from derivations in
the measurements (see Figure 2). Configuration F shows a large
difference between derived thermal capacitances. The cause for
this is presently unclear.


The same mock-up system is used as was used in previously
described temperature measurements. The emissivity of materials in the mock-up system is not similar, especially differences
between polystyrene and polished aluminum. In order to obtain
comparable results, the device has been uniformly colored with
hydrated magnesium silicate powder (talc powder), shown on
the left side of Figure 13 to determine uniform emissivity of
different materials used. However, applying a coating on the
surface of the aluminum encasing does influence heat transfer
through radiation due to changes in emissivity. This mock-up
has been modified with one transparent side, enabling individuals to see inside the device. This was also included to keep
temperature distribution as realistic as possible (especially for
configuration A) by preventing ventilation through the product.
Two different configurations, namely, closed and open encasings, respectively A and B, have been analyzed using infrared
measurements. The two materials tested include polystyrene and
aluminum.
Figure 13 shows results for four experiments. The experiments encompass both configurations A and B (closed and
open encasings), using both polystyrene and aluminum encasing material. The results show the influence encasing material
has on temperature distribution along the encasing surface and
the reduction in hotspot temperature experienced by ventilation. Ambient temperature Ta and hotspot temperature Th have
Table 4 Total thermal resistance R [K/W]

Table 3 Time constants X = RC [s]
Configuration
PS A
Al A
PS B
Al B
PS C
Al C
PS D

Al D
PS E
Al E
PS F
Al F

Configuration

0.25 W

0.5 W

1.0 W

767
742
601
708
893
749

746
835
695
620
885
751

767
819

661
562
822
761
219
200
643
518
425
509

662
167

678
560
490
485

2.0 W

308
183

5.0 W

248
216

0.25 W


0.5 W

1.0 W

40
42
39
36
26
23

38
40
36
33
23
22

35
38
33
31
21
20
5
5
24
11
16

15

2.0 W

5.0 W

7.5 W

5
4

4
4

4
4

7.5 W

230
205

606
586

Polyst. A
Alum. A
Polyst. B
Alum. B
Polyst. C

Alum. C
Polyst. D
Alum. D
Polyst. E
Alum. E
Polyst. F
Alum. F

27
13

24
12
21
18

Note. Polyst., polystyrene; alum., aluminum.

heat transfer engineering

vol. 31 no. 6 2010

15
13


R. STRIJK ET AL.
Table 5 Thermal capacitance C [J/K]
Configuration
Polyst. A

Alum. A
Polyst. B
Alum. B
Polyst. C
Alum. C
Polyst. D
Alum. D
Polyst. E
Alum. E
Polyst. F
Alum. F

Table 6 Infrared results

0.25 W

0.5 W

1.0 W

19
18
15
20
34
33

20
21
20

19
38
34

22
22
20
18
38
38
44
42
27
45
26
35

24
13

28
46
23
26

443

2.0 W

5.0 W


7.5 W

Configuration
PS A
PS B
Al A
Al B

Ta [◦ C]

Th [◦ C]

Th − Ta [K]

21
20
21
18

34
31
33
27

13
12
12
9


Note. PS, polystyrene; Al, aluminum.
68
42

56
58

55
57

41
45

Note. Polyst., polystyrene; alum., aluminum.

been obtained using measurements determined by means of
software, which is compatible with the infrared thermography
camera ThermaCAM Researcher [17]. The results are given in
Table 6. An encasing with a higher level of thermal conductivity
shows a lower hotspot temperature, in this case, Th − Ta = 12
K for aluminum versus Th − Ta = 13 K for polystyrene with
configuration A and Th − Ta = 12 K versus Th − Ta = 9 K for
configuration B. Ventilation holes appear to have an improved
effect on the hotspot temperature for this mock-up system.

PRACTICAL APPLICATION
Model 1
Model 1, presented in Figure 14, gives guidelines that can
be used to evaluate whether passive cooling for a product is


feasible. These guidelines can be applied by estimating power
consumption and the surface area of the minimum enclosing
box. Depending on the type of product, the probability that a
critical hotspot temperature will occur in the design may be
predicted.
The application of this model is twofold. First, the model is
to be used during the very early stages of design (conceptual
phase) to gain insight into whether or not the use of active cooling is necessary. The designer begins by defining the ratio q/A.
Then, he or she continues with positioning the design in the
graph or comparing the results to the rule of thumb, described
earlier. The analysis ends when a decision is made on whether or
not a fan will be used in the design (active cooling) and with an
assessment of whether a detailed thermal analysis in subsequent
design phases is needed. Second, the rule of thumb can be used
as a means of communication between design and electronics
engineers. The design team can use the graph to benchmark its
products, comparing them to those of competitors, and define
targets with regards to new or developed products. For comparable studies, see Yazawa and Bar-Cohen [5].
In some cases, a graph can be difficult to read, especially
when products are on the boundary line between two areas.
Therefore, a new measure is proposed that equals the ratio q/A.
If the ratio q/A changes when compared to previous designs

Figure 13 Results of the infrared (IR) experiment.

heat transfer engineering

vol. 31 no. 6 2010



444

R. STRIJK ET AL.

Figure 14 Model 1.

through either an increase in power consumption or a reduction
in product surface area, then the designer and electronic engineer must again assess the product on the basis of the rule of
thumb and estimate whether or not a change in design or a more
extensive thermal analysis is required.
By examining temperature lines, corresponding ratios of q/A
can be derived. These include 5 K, with a ratio of q/A ≈ 50,
15 K, with a ratio of q/A ≈ 150, and 25 K, with a ratio of
q/A ≈ 300. The designer can obtain some insight on whether
a detailed analysis of temperatures within the product is necessary, based on a simple rule of thumb. However, the following
does not apply to the development of heating products (e.g.,
toaster, watercooker, etc.). A different approach other than that
presented here must be taken into account. The model is applied
as follows for a given design:
1. Estimate q and A of your design.
2. Determine in which of the zones in Figure 14 your design is
positioned.
a. If q/A > 300, the design lies in zone 1 and active cooling,
with a detailed thermal analysis, is essential.
b. If 300 > q/A > 150, the design lies in zone 2 and active
cooling can be used with a low thermal risk.
c. If 150 > q/A > 50, the design lies in zone 3 and passive
cooling is an option, but a detailed thermal analysis is
essential.
d. If 50 > q/A, the design lies in zone 4 and the product

can be passively cooled.
3. Make decisions, set criteria and reuse the model when significant design changes in q or A occur.

Model 2
On the basis of Eq. (4), a software program can easily be developed that computes required parameters. The authors of this
study have developed such a software program, named Thermanizer, which numerically solves the system (Figure 15). The
model can now be easily applied to a given design by using the
following requirements:
heat transfer engineering

Figure 15 Numerical solver Thermanizer.

1.
2.
3.
4.

Gather the required design parameters.
Start the software program and fill in required variables.
Run the program.
Use the results to make design decisions and evaluate design
changes.

Figure 16 shows the results of Thermanizer. The absolute temperatures can be derived from these values by using
proper addition. The temperature differences are described as
follows:
•
•
•
•


Core of the hotspot to hotspot encasing Tc − Th .
Hotspot encasing to inside encasing Th − Ti .
Inside encasing to outside encasing Ti − Te .
Outside encasing to the ambient environment Te − Ta .

The present state of development for a software program is
currently reliable enough for usability research, which is the
main motivation for its development. It is recommended, if the
application is successful, to extend the program using additional
product configurations, including a valid area of application for
each addition. Developing possibilities that would include use
scenarios in order to improve transient analysis is also recommended.

Model 3
In this section, a description is given of the practical use of
the mathematical model, Eq. (5), as a standard formula in the
design of an electronic product. The method is presented as a
stepwise plan that is easy to understand and should be applied
as follows:
1. Measure the hotspot temperature, average encasing temperature, and the ambient temperature every minute until the
temperature has reached an approximate steady state. Also,
measure the amount of dissipated power coming from the device. It is advisable to choose dissipated power such that the
vol. 31 no. 6 2010


R. STRIJK ET AL.

445


Figure 16 Graphs produced by Thermanizer.

2.

3.
4.

5.

temperature of the hotspot reaches its approximate maximum
allowable value.
Derive the steady-state temperature and time constant X from
the measurements. X = RC occurs at approximately the same
time as when the temperature of the hotspot reaches 63% of
its steady-state value.
Derive the thermal resistance and thermal capacitance using
a
and C = X
the following equations: R = Tm −T
q
R
Use the R and C values to calibrate the general equation
−t
T (t) = Tm − e( RC ) (Tm − Ta ). Set up the matrix equations to
calculate hotspot and encasing temperatures.
Use the equation to study design changes.

Example
In this section, model 3 and its method for application are
applied to the variable mock-up system. The model is first calibrated using results from the measurements shown in configuration A, which was executed using polystyrene with a 0.5-W

power dissipation. Then, the calibrated model is used to predict
the effects of design changes on configurations A, B, C, D, E,
and F, with 1 W power dissipation. These results are compared
to the measurement data shown in Figure 17.
Step 1. In a mock-up for a design, measure the hotspot, average encasing and ambient temperatures. Measurements are presented for Th , Te , and Ta . Configuration
heat transfer engineering

Figure 17 Comparison of measurements and predictions for configuration A
with a 0.5-W power dissipation.

vol. 31 no. 6 2010


446

R. STRIJK ET AL.

Figure 18 Comparison of measurements and predictions for configuration A, B, C, D, E, and F.

A uses polystyrene material for the encasing and sets
the calibration at 0.5 W. For power dissipation, see
Figure 17.
Step 2. Derive the steady-state temperature and time constant
X from the measurements. The time constant for this
configuration has been derived and is given in Table 3:
X= 746 s.
Step 3. Derive the thermal resistance. The following values
for R and C are given in Table 4 and Table 5: R =
38 K/W and C = 20 J/K. The following measurement
for thermal resistance R3 is derived from the average

steady-state encasing temperature (Figure 12): R3 =
(Te − Ta )/q = 10 K/W. The following measurement for
thermal resistance inside the configuration R2 results
from differences between R and R3 : R2 = R − R3 =
28 K/W. Finally, the following thermal resistance R1
will be set to equal infinity, since the model is calibrated
for a fully closed encasing, R1 = ∞ K/W.
Step 4. Calibrate the general equation. The results of the calibrated model are shown in Figure 17. Since the model
is calibrated for a fully closed encasing, the following
heat transfer engineering

matrix equation is used:
Th (t)
Te (t)

=

Ta
Ta

+

R2 + R3
R3

R2 + R3
R3

q
−t

−qe( RC )

Step 5. Based on the calibrated model, predictions are made for
all configurations with a power dissipation of 1.0 W. Results
are compared to measurements for a polystyrene encasing
and given in Figure 18. A summary of the variables and values
used in the predictions is given in Table 7. The predictions
have been completed using the following assumptions:
PS A-1.0 Predicted by changing levels of power dissipation q to
1.0 W.
PS B-1.0 In this prediction, R1 thermal resistance is added because the configuration is open and dissipation to the ambient environment must be taken into account. R1 is estimated by taking into account the top area A = 2.4 ×
10−2 × 3 × 10−2 = 7.2 × 10−4 m2 of the hotspot and the
heat transfer coeffcient hc = 10 W/m2 K: R1 = 1/(hc A) =
139 K/W.
vol. 31 no. 6 2010


R. STRIJK ET AL.
Table 7 Variables and values used in predictions
Variable
X [s]
q [W]
R [K/W]
R1 [K/W]
R2 [K/W]
R2 [K/W]
C [J/K]

PSA0.5 PSA1.0 PSB1.0 PSC1.0 PSD1.0 PSE1.0 PSF1.0
746

0.5
38
∞
28
10
20

746
1.0
38
∞
28
10
20

597
1.0
30
139
28
10
20

355
1.0
18
33
28
10
20


61
1.0
3
3
28
10
20

206
1.0
10
∞
0
0
20

256
1.0
13
∞
3
10
20

PS C-1.0 For these predictions, R1 thermal resistance is added
because the configuration is open and dissipation to the ambient environment must be taken into account. In this configuration, five cooling fins have been added. R1 is estimated
using the surface area of the cooling fins A = 2 × 5 × 1 ×
10−2 × 3 × 10−2 = 3 × 10−3 m2 and hc = 10 W/m2 K. This
results in a thermal resistance of R1 = 1/(hc A) = 33 K/W.

PS D-1.0 For the following predictions, R1 thermal resistance
is added because the configuration is open and dissipation to
the ambient environment must be taken into account. Cooling fins are attached to the hotspot. R1 is therefore estimated
as having an area of A = 2 × 5 × 1 × 10−2 × 3 × 10−2 =
3 × 10−3 m2 . For forced convection, a heat transfer coefficient hc = 100 W/m2 -K is proposed. The results for thermal
resistance are R1 = 1/(hc A) = 3 K/W.
PS E-1.0 For predictions, the R2 thermal resistance is changed
because the hotspot is attached to the encasing. Between
the hotspot and encasing a thermal conductive foil has been
used with a thermal conductivity of k = 0.9 W/m-K and a
thickness of x = 0.2 × 10−3 m. The surface area is the same
as in configuration PS B, A = 2.4 × 10−2 × 3 × 10−2 = 7.2
× 10−4 m2 , which results in thermal resistance R2 = x/(kA)
= 0.3 ≈ 0 K/W.
PS F-1.0 These predictions incorporate changes in R2 because
a fan is added inside the mock-up. A forced convection heat
transfer coefficient of 100 W/m2 -K is therefore proposed.
This results in a thermal resistance of R2 = 2.8 ≈ 3 K/W,
which is 10 times smaller than those proposed in configuration A.

CONCLUSIONS
In this article, three models have been proposed to help solve
specific issues in the thermal design of electronic products.
Model 1 is regarded as generally valid for electronic products used under normal conditions. Exceptions include products that must work in extreme ambient conditions, such as
those operating at high altitudes, outdoors, or with specific ergonomic requirements regarding encasing temperatures. Important guidelines for applying this model include the realization
that it does not prevent occurrences of or solutions for local
hotspots. Model 2 can compute hotspot temperature with an accuracy of 20%, which is accurate enough to evaluate structural
heat transfer engineering

447


concepts during early design stages. However, this model only
discusses the heat path for one single hotspot and, therefore,
cannot be generally applied to all products. The need for development and verification of similar models with the ability to
locate several hotspots has been advised by several participants
during interviews and is suggested for consideration in future
research. Model 3 is seen as a valid method for approximating
temperatures in steady-state situations, once boundary conditions have been calibrated using measurements obtained from
a thermal mock-up for a functional model. Global thermal capacitance can be derived from measurements using the transient
behavior of a specific heat path by means of the unconstrained
minimization method. However, the model does not support
transient behavior for devices in which there are significant differences in time constants. Completing a curve-fitting analysis
using detailed RC networks is suggested.

NOMENCLATURE
C
cp
F1,2
g
Gr
H
k
L
Nu
Pr
q
R
Ra
T
W

x

thermal capacitance, J/K
specific heat, J/kg-K
view factor
gravitational acceleration, m/s2
Grashoff number, L3 ρ2 βg T /µ2
height, m
thermal conductivity, W/m-K
characteristic dimension, (W + H)/2,m
Nusselt number, 0.54Ra0.25
Prandtl number, cp µ/k
power dissipation, heat flow, W
thermal resistance, K/W
Rayleigh number, GrPr
temperature, ◦ C, K
width, m
time constant, s

Greek Symbols
β
ε
µ
ρ
σ
υ

temperature coefficient of volume expansion, 1/K
emissivity of radiating surface
absolute viscosity, N-s/m2

density air, kg/m3
Stefan–Boltzmann constant, W/m2 -K4
kinematic viscosity, m2 /s

Subscripts
a
av
air
e
s

refers to ambient
refers to average
refers to air properties
refers to encasing
refers to surface
vol. 31 no. 6 2010


448

R. STRIJK ET AL.

REFERENCES
[1] Smith, P., and Reinertsen, D., Developing Products in Half the
Time; New Rules, New Tools, Van Nostrand Reinhold, New York,
1998.
[2] Weiser, M., The Computer for the 21st Century, Scientific American, vol. 265, no. 3, pp. 94–104, 1991.
[3] Joshi, Y., Azar, K., Blackburn, D., Lasance, C., Mahajan, R., and
Rantala, J., How Well Can We Assess Thermally Driven Reliability Issues in Electronic Systems Today? Summary of Panel Held

at the Thermal Investigations of ICs and Systems (Therminic),
Microelectronics Journal, vol. 34, no. 12, pp. 1195–1201, 2002.
[4] Ishizuka, M., Hayama, S., and Iwasaki, H., Application of a
Semi-Empirical Approach to the Thermal Design of Electronic
Equipment, 7th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITHERM), May
23–26, Las Vegas, NV, pp. 99–106, 2000.
[5] Yazawa, K., and Bar-Cohen, A., Energy Efficient Cooling of Notebook Computers, 8th Intersociety Conference on Thermal and
Thermomechanical Phenomena in Electronic Systems (ITHERM),
May 30–June 1, San Diego, CA, pp. 785–791, 2002.
[6] Strijk, R., de Deugd, J. A. G., and Vergeest, J. S. M., Passive or Active Cooling: A Model for Fast Thermal Exploration of Electronic
Product Concepts, Thermal Challenges in Next Generation Electronic Systems II (THERMES II), January 13–16, pp. 415–422,
Santa Fe, NM, Rotterdam, Millpress, 2007.
[7] Strijk, R., Raangs, A., de Deugd, J. A. G., and Vergeest, J. S. M.,
Fast Thermal Exploration in the Preliminar Design of Electronic
Products, 16th International Conference on Engineering Design
(ICED), August 28–31, pp. 39–40, Paris, France, 2007.
[8] Strijk, R., Conceptual Thermal Design, Ph.D. thesis, Delft University of Technology, Faculty of Industrial Design Engineering,
Delft, Netherlands, 2008.
[9] Strijk, R., de Deugd, J. A. G., and Vergeest, J. S. M., Quick
estimation of hotspot temperature and encasing temperature of an
electronic product, 19th National & 8th ISHMT-ASME Heat and
Mass Transfer Conference, January 3–5, Hyderabad, India, 2008.
[10] Strijk, R., Deugd, J. A. G. de., and Vergeest, J. S. M., Simple
Thermal Modeling of Hotspot and Encasing Temperature of Electronic Product Designs, 19th National & 8th ISHMT-ASME Heat
and Mass Transfer Conference, January 3–5, Hyderabad, India,
2008.
[11] Strijk, R., Vergeest, J. S. M., and Brezet, J. C., Quick Estimation
of Temperature in Electronic Products, Proceedings of the 7th
International Symposium on Tools and Methods of Competitive


heat transfer engineering

[12]
[13]

[14]

[15]

[16]
[17]

Engineering (TMCE), April 21–25, eds. I. Horv´ath and Z. Rus´ak,
pp. 691–704, Izmir, Turkey, 2008.
Remsburg, R., Thermal Design of Electronic Equipment, CRC
Press, Boca Raton, FL, 2001.
Karnopp, D., Margolis, D. L., and Rosenberg, R. C., System Dynamics: A Unified Approach, John Wiley & Sons, New York,
1990.
Teertstra, P., Yovanovich, M. M., and Culham, J. R., Modeling
of Natural Convection in Electronic Enclosures, 9th Intersociety
Conference on Thermal and Thermomechanical Phenomena in
Electronic Systems (ITHERM), June 1–4, Las Vegas, NV, pp. 140–
149, 2004.
Infrared Services, Inc., Emissivity Values for Common Materials,
, date of access April 29,
2008.
Holman, J. P., Heat Transfer, McGraw-Hill, Boston, 2002.
FLIR Systems, Thermacam researcherTM , , date of access April 29, 2008.
Ruben Strijk is an assistant professor in the Design
Engineering research group at the Delft University

of Technology, Delft, The Netherlands. He received
his Ph.D. in Industrial Design Engineering from the
Delft University of Technology in 2008. His research
interests involve thermal design, energy efficiency,
and renewable energy applied to the field of design
engineering.

Han Brezet is a professor of the Design for Sustainability Program at the Delft University of Technology,
Delft, The Netherlands. He received his Ph.D. in environmental sociology from the Rotterdam Erasmus
University in 1993. His research interests involve the
developments of theory and tools that help industry to
develop sustainable products and so improving product development in an ecological, economical, and
sociological sense.
Joris Vergeest is an associate professor in the Computer Aided Design and Engineering research group
at the Delft University of Technology, Delft, The
Netherlands. He received his Ph.D. in experimental
physics from the Radboud University Nijmegen in
1979. His research interests involve design engineering with a main focus on computer-aided design.

vol. 31 no. 6 2010


Heat Transfer Engineering, 31(6):449–457, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903408334

Correlation for Heat Transfer in
Nucleate Boiling on Horizontal
Cylindrical Surface

P. K. SARMA,1 V. SRINIVAS,2 K. V. SHARMA,3 and V. DHARMA RAO4
1

International Academic Affairs, GITAM University, Rushikonda, Visakhapatnam, India
Department of Mechanical Engineering, GITAM University, Visakhapatnam, India
3
Faculty of Mechanical Engineering, Universiti Malaysia Pahang, Pahang, Malaysia
4
Department of Chemical Engineering, A.U. College of Engineering, Visakhapatnam, India
2

This experimental investigation deals with nucleate boiling studies on horizontal cylindrical heating elements made out of
copper in the medium of Forane around atmospheric conditions. The data could be successfully correlated with the system of
criteria employed by the authors in their earlier study of nucleate boiling process on cylindrical heating elements. Inclusion
of the data from the present experimental study on Forane and that of other investigators yielded a comprehensive correlation
with an average deviation of 20% and standard deviation of 25% over a wide range of system pressures.

INTRODUCTION

Pioro et al. [29, 30] as

Studies on nucleate boiling are quite extensive in the heat
transfer literature [1–31]. Rohsenow and his co-investigators [4,
16, 17] in their pioneering studies proposed the correlation
q
µl hfg

σ
g(ρl − ρv )


1/2

1
=
Csf

1/r

Pr−s/r

Cpl [Tw − Ts ]
hfg

1/r

(1)
The constant Csf in the correlation is an important characterizing parameter that varies with surface–liquid combination. The
values of variable constants Csf , s, and r can be obtained from
heat transfer handbooks.
Pioro et al. [29, 30] concluded that Eq. (1) is the best among
the existing correlations. However, the constant Csf is to be
amended depending on the roughness factor and the liquid–
surface combination. A modification of Eq. (1) is presented by

hl ∗
∗
N u=
= Csf
kl


hfg ρv0.5 σ g (ρl − ρν )

Prm (2)

0.25

∗
The values of Csf
and m in Eq. (2) are to be chosen based on
the surface roughness factor and liquid medium–surface combination. Correlations presented by various authors [6, 9, 11–15,
18, 19] are also useful for the estimation of nucleate boiling heat
transfer coefficients. Of these, the equations of Labuntsov [18,
19] and Kruzhilin [1, 2], given respectively as

ρv
h = 0.075 1 + 10
(ρl −ρv )

2
3

kl2
νl σTS

1
3

2

(3)


q3

and
hl ∗
= 0.082
kl

The first two authors acknowledge the support received from Dr. M. V. V. S.
Murthi, President of GITAM University. The financial support for the procurement of experimental setup received from TEQIP, World Bank, by the Centre
for Energy Studies, JNTU College of Engineering, is acknowledged.
Address correspondence to Dr. P. K. Sarma, International Academic Affairs, GITAM University, Rushikonda, Visakhapatnam 530045, India. E-mail:


2/3

q

ρv
(ρl − ρv )

hfg q
g (TS + 273.15) kl

⎛

⎞0.33

⎜ (TS + 273.15) CP σ ρl ⎟
×⎝

0.5 ⎠
σ
(hfg ρv )2 (ρ −ρ
)g
l

Pr−0.45

v

are used in the present analysis for comparison.

449

0.7

(4)


450

P. K. SARMA ET AL.
Table 1 Specifications of the experimental setup

PRESENT ANALYSIS
In a recent paper, Sarma et al. [31], making use of the dimensionless criteria, developed a correlation valid for a wide range
of system conditions using the data of Borishansky et al. [6].
The choice of dimensionless criteria is based on the analyses of
previous investigators wherever applicable. From Rohsenow’s
[4] turbulent

convective analogy, the modified Reynolds num∗
ber µq hl fg is considered a significant π parameter where l∗ is the
l
characteristic length. The choice of l∗ may be the diameter of
σ
the emerging bubble i.e. C (ρ −ρ
)g where the value of C can
l

A new π term, (

P δt l ∗
, ,
Pcr D D

PD
1/2 )
µl hfg

σ
(ρl − ρv )g

(5)

introduced into the existing system

and its significance has been explained in [31]. The resulting
correlation is obtained with an average and standard deviation
as 16% and 22%, respectively,
q

µl hfg

σ
= 3.8 × 10−6
(ρl − ρv )g
×

PD

Forane (R141b)

Material of the test surface
Critical pressure of fluid
Diameter of the test section
Length of the test section
Effective surface area
Maximum permissible temperature
Pressure ranges
Heater capacity

Copper
43 bar
12.7 mm
42 mm
0.018 m2
220◦ C
–150 to 350 kPa (gauge)
600 W

v


be included in the constant of multiplication to be finally arrived
at in the dimensionless correlation.
Mostinski [9] and Borishansky [15] suggested that a better
correlation can be achieved by introducing PPcr as an important
thermodynamic consideration. Hence, significance is given to
this ratio in the analysis.
Tien et al. [8] considered the nucleate boiling heat transfer
as inverted stagnation flow normal toward the wall. Hence, δDt
is considered as another important π group where δt is the
thickness of thermal boundary layer, which can be of the order
of magnitude given by δt = ( qTwkl ). Thus the present analysis
pivots around the choice of the following three dimensionless π
groups:
ql ∗
=f
µl hfg

Fluid

D
δt
0.55

1/2

µl hfg

1.22


P
Pcr

0.72

σ
(ρL − ρv )gD 2

260 mm < L < 300 mm
Material: 18% Ni, 8% Cr steel
It is observed that nucleate boiling experimental data with the
Forane–copper combination are not available in the literature.
The present study is organized to evaluate whether the correlations commonly cited in nucleate boiling literature can be
employed to estimate the heat transfer coefficients for copper–
Forane [R-141b] surface–liquid combination and for a wide
range of system parameters.

DESCRIPTION OF EXPERIMENTAL SETUP
Experiments are conducted on a prefabricated nucleate boiling heat transfer test rig manufactured by M/s P. A. Hilton,
UK. The salient specifications of the equipment are mentioned
in Table 1. The schematic diagram of the test rig shown as
Figure 1 consists of a thick walled glass chamber of 80 mm
bore and 300 mm long. The chamber houses the heating element with a condenser coil placed above the free surface of the
liquid bulk. The heating element is a 600-W cartridge heater

1.65

(6)
and valid for the following ranges of parameters:
Fluid: water:

1 bar < P < 200 bar [Pcr = 221 bar]
4.9 mm < D < 6.94 mm
260 mm < L < 262 mm
Material: 18% Ni, 8% Cr steel
Fluid: ethyl alcohol:
1 bar < P < 60 bar [Pcr = 64 bar]
4.9 mm < D < 6.94 mm

Figure 1 Schematic of the nucleate boiling test rig.

heat transfer engineering

vol. 31 no. 6 2010


P. K. SARMA ET AL.

451

Table 2 Summary of ranges of experimental results in the present
study
Pressure
Wall Temperature
Wall heat flux
Heat transfer coefficient
Bulk temperature

1.3 to 2.2 bar
50 to 75◦ C
27 to 188 kW/m2

3.2 to 15.8 kW/m2 −◦ C
40 to 56◦ C

swaged into the copper test section to dissipate heat flux uniformly. The test section is a copper tube of diameter 12.7 mm
and length 42 mm with an effective surface area of 0.018 m2 .
The orientation of test section is horizontal. The test section
is submerged in a pool of Forane (R-141b) liquid. Over the
test surface, six thermocouples are preened at regular intervals and the average of these values can be read with the aid
of digital temperature indicator. A phase angle controller to
give infinitely variable heat input to the test section accomplishes the heating. The heat transfer rate can be read from a
digital wattmeter. The heat flux is calculated using the relaQ
where Q is the wattmeter reading and D the
tion q = πDL
outer diameter of the tube. The condenser located in the free
vapor space is made of 9 coils of nickel coated copper tube
with a total surface area of 0.032 m2 . The condenser coil condenses the vapor produced by the test surface and the condensate returns to the bottom of the chamber by gravity. The pressure in the chamber is controlled by varying the cooling water
flow rate to the condenser. A glass thermometer is mounted
in the bulk of the liquid to measure the liquid bulk or saturation temperature TB corresponding to the system pressure.
The heat transfer coefficient is calculated from the equation
h = q (Tw − Tb ). The unit can also be interfaced to a computer and parameters like heat flux q, temperature difference
T , wall temperature TW , gauge pressure Pg , and heat transfer
coefficient h automatically registered for various heat inputs.
All measuring instruments are of class I type and the error
will not be more than ±3%. The surface roughness of the test
section is not available. Extensive experimentation had been
done on the test rig and the summary of the range of applicability is given in Table 2. The results obtained from the test
setup for various system pressures are tabulated as entries in
Table 3.

Figure 2 Comparison of the experimental data of Borishansky et al. [6] and

present data with correlation using Eq. (7).

20%:
q
µl hfg

σ
= 5.02 × 10−7
(ρl − ρv )g
×

In an attempt to validate the criteria proposed by the
authors, the data of Borishansky et al. [6] along with
the present experimental data are shown plotted in Figure 2. The entire set of data comprising 575 points could
be successfully correlated by the following equation with
a standard deviation of 25% and average deviation of
heat transfer engineering

0.63

1/2

µl hfg

1.23

−0.969

P
Pcr


σ
(ρl − ρv )gD 2

1.25

(7)

In general, the correlations of various authors indicate that
the heat transfer coefficient is independent of the diameter of
the tube. Hence to check the possibility of correlating the data
in terms of the characteristic diameter of the bubble l ∗ , the
experimental data is subjected to regression analysis for the
following system of criteria:
ql ∗
=f
µl hfg

l∗
δt

,

P
Pcr

,

P l ∗ 1/2
h

µ l fg

(8)

The resulting correlation for the entire range of experimental
data with water, ethyl alcohol, and Forane is obtained as
ql ∗
= 3.36 × 10−5
µl hfg

CORRELATION OF THE DATA

PD

D
δt

l∗
δt

1.18

P
Pcr

−0.58

P l∗
1/2


µl hfg

0.406

(9)

with a standard deviation (SD) of ±38% and average deviation
(AD) of ±27%. However, the scatter of the data from the mean
line is found to be more with the exclusion of the diameter of
the heater element in the system of criteria. Figure 3 shows
the validation of the correlation Eq. (9) for the three fluids
investigated with different surface–fluid combinations.
vol. 31 no. 6 2010


452

P. K. SARMA ET AL.

Table 3 Experimental data
Ps bar

T◦W C

T ◦C

1.379
1.392
1.404
1.418

1.443
1.443
1.451
1.451
1.459
1.467
1.475
1.491
1.507
1.515
1.563
1.563
1.587
1.595
1.601
1.603
1.603
1.611
1.611
1.619
1.627
1.643
1.659
1.667
1.675
1.683
1.683
1.691
1.699
1.699

1.707
1.707
1.715
1.715
1.731
1.739
1.755
1.763
1.763
1.779
1.787
1.787
1.795
1.795
1.811
1.819
1.835
1.835
1.867
1.875
1.875
1.883
1.899
1.899
1.907
1.915

49.20
50.12
51.54

51.84
52.81
53.37
53.74
53.52
54.68
55.12
55.71
57.18
58.12
54.73
57.78
54.86
55.84
58.37
57.84
57.32
56.84
57.84
60.13
56.24
61.60
61.60
57.23
62.59
59.67
58.70
58.76
60.66
58.24

57.16
59.68
58.72
59.71
58.75
61.80
63.74
65.81
60.83
59.86
66.16
62.19
60.36
60.83
62.42
62.59
64.24
67.16
69.09
67.85
62.59
62.82
71.51
64.75
63.79
64.79
77.32

8.75
7.85

8.95
8.75
8.71
10.71
9.72
9.14
9.73
7.74
10.21
8.76
8.76
9.24
11.29
8.27
8.75
8.67
10.21
9.73
9.24
9.22
12.64
8.27
13.10
13.93
8.76
13.13
10.71
9.73
9.24
11.68

8.76
8.27
10.21
9.24
10.22
9.24
14.10
13.61
15.24
10.21
9.24
15.05
12.19
9.25
9.73
10.24
11.68
12.64
15.32
10.11
14.22
10.21
10.21
18.40
12.74
10.69
12.14
24.19

heat transfer engineering


qW W/m2

T◦b C

h W/m2◦ C

27980
29810
32560
34520
42900
44440
46120
45120
47250
48870
50140
52270
55390
56230
60140
61240
65490
69120
71240
75270
76320
78210
80240

81250
82910
84580
88620
89650
90920
93270
92670
94280
95630
95320
98320
99210
101240
101850
102560
103240
105630
106350
105680
107680
108920
110210
114270
113620
115370
118650
125680
126210
136240

137240
138850
139120
140870
141360
143120
145970

40.45
42.27
42.59
43.09
44.10
42.66
44.02
44.38
44.95
47.38
45.50
48.42
49.36
45.49
46.49
46.59
47.09
49.70
47.63
47.59
47.60
48.62

47.49
47.97
48.50
47.67
48.47
49.46
48.96
48.97
49.52
48.98
49.48
48.89
49.47
49.48
49.49
49.51
47.70
50.13
50.57
50.62
50.62
51.11
50.00
51.11
51.10
52.18
50.91
51.60
51.84
58.98

53.63
52.38
52.61
53.11
52.01
53.10
52.65
53.13

3197.71
3797.45
3637.99
3945.14
4925.37
4149.39
4744.86
4936.54
4856.12
6313.95
4910.87
5966.89
6323.06
6085.50
5326.84
7405.08
7484.57
7972.32
6977.47
7735.87
8259.74

8482.65
6348.10
9824.67
6329.01
6071.79
10116.44
6827.88
8489.26
9585.82
10029.22
8071.92
10916.67
11526.00
9629.77
10737.01
9906.07
11022.73
7273.76
7585.60
6931.10
10416.26
11437.23
7154.82
8935.19
11914.59
11744.09
11095.70
9877.57
9386.87
8203.66

12483.68
9580.87
13441.72
13599.41
7560.87
11057.30
13223.57
11789.13
6034.31
(Continued on next page)

vol. 31 no. 6 2010


P. K. SARMA ET AL.

453

Table 3 Experimental data (Continued)
Ps bar

T◦W C

T ◦C

1.915
1.931
1.947
1.979
1.979

1.987
1.987
2.003
2.009
2.019
2.019
2.027
2.035
2.043
2.044
2.051
2.059
2.067
2.067
2.067
2.067
2.075
2.075
2.075
2.079
2.083
2.091
2.091
2.091
2.099
2.099
2.115
2.123
2.131
2.155

2.171
2.187
2.187
2.203

66.73
73.48
71.07
65.77
78.30
66.73
72.51
77.39
73.96
62.71
65.74
79.20
72.06
67.27
77.36
77.43
70.14
69.65
67.24
79.30
67.73
74.60
71.12
74.32
69.85

70.14
67.74
76.42
79.34
67.27
71.32
69.23
74.09
74.61
75.12
76.11
75.75
74.80
75.19

13.10
19.36
17.24
11.65
23.69
12.12
17.54
23.31
19.35
12.65
11.07
23.60
16.46
11.00
21.27

19.83
19.83
14.05
11.15
23.20
11.63
18.86
14.52
17.89
13.07
14.00
11.14
19.82
22.71
10.66
14.99
14.06
16.93
17.89
18.85
18.85
18.37
18.37
18.85

Note. PS , system pressure; TW , wall temperature;

qW W/m2

T◦b C


h W/m2◦ C

148260
151210
153230
155690
156320
158950
163530
163260
164850
165170
164060
165210
166320
168210
168950
170320
171350
172350
173860
174350
173340
174350
175950
174240
175270
176420
177010

177150
177630
178240
178680
181240
182340
183540
185340
186980
188390
187350
188890

53.63
54.12
53.83
54.12
54.61
54.61
54.97
54.08
54.61
50.06
54.67
55.60
55.60
56.27
56.09
57.60
50.31

55.60
56.09
56.10
56.10
55.74
56.60
56.43
56.78
56.14
56.60
56.60
56.63
56.61
56.33
55.17
57.16
56.72
56.27
57.26
57.38
56.43
56.34

11317.56
7810.43
8888.05
13363.95
6598.56
13114.69
9323.26

7003.86
8519.38
13056.92
14820.23
7000.42
10104.50
15291.82
7943.11
8589.01
8640.95
12266.90
15592.83
7515.09
14904.56
9244.43
12117.77
9739.52
13410.10
12601.43
15889.59
8937.94
7821.66
16720.45
11919.95
12890.47
10770.23
10259.36
9832.36
9919.36
10255.31

10198.69
10020.69

T = (TW – TB ); qw , wall heat flux; Tb , bulk temperature; and h, heat transfer coefficient.

COMPARISON OF DATA WITH CORRELATIONS OF
OTHER INVESTIGATORS
The present data are shown plotted with the often-cited correlations on nucleate boiling. None of the correlations could
satisfactorily agree with the present data taken with the Forane–
copper combination. However Rohsenow’s Eq. (1) is shown
plotted along with the present data Figure 4. For the choice of
Csf = 0.0026, r = 0.33, and s = 2, the data could be correlated
satisfactorily. These constants are quite close to the prescribed
values for the R113–copper combination as originally suggested
by Rohsenow and co-investigators [4, 16, 17]. Similarly, Eq.
(3) developed by Labuntsov [18, 19] revealed substantial disagreement with the present data as shown in Figure 5. The
heat transfer engineering

constant 0.075 in the equation when replaced with 0.0215 has
yielded better agreement with the data as shown in Figure 6.
Equation (4) of Kruzhilin [1, 2] as postulated by their original
analysis has deviated considerably from the present data. Replacing the constant in Eq. (4) with 1.64, better agreement can
be observed, as is evident from Figure 7.

SIGNIFICANCE OF THE NEW DIMENSIONLESS TERM
The significance of the dimensionless term (

PD
1/2 )
µl hfg


is shown

in Figure 8 and can be well understood by expanding it as a
vol. 31 no. 6 2010


454

P. K. SARMA ET AL.

Figure 4 Comparison of the present experimental data with Eq. (1) of
Rohsenow et al. [4, 16, 17].
Figure 3 Comparison of the experimental data of Borishansky et al. [6] and
present data with correlation using Eq. (9).

such that π3 denotes the influence of the thermal aspects associated with liquid vaporization responsible for the growth of the
bubble. V can be viewed as the velocity of the bubble growth,
given by V = dD/dt.
The term ( PD1/2 ) gives the combined influence of dynamics

product of three dimensionless π groups.
PD
1/2

µl hfg

=

P D2

ρl D 2 V 2

ρl V D
µl

V2
hfg

1/2

= π1 π2 π3

µl hfg

of the bubble growth with the thermal effects in the thermal
(10)

The physical significance of various π parameters is as follows:
π1 =

P D2
Pressure force
=
2
2
ρl D V
Inertia force of the bubble

(11)


where π1 is the modified Euler’s number, denoting the dynamics
of bubble growth, and
π2 =

Indertia force
V Dρl
=
µl
Viscous force

(12)

is the modified Reynolds number. Further, π2 denotes the dynamics of flow of the surrounding fluid during the bubble dilatation. Also,
π3 =

=

V2
hfg
Energy associated with dilation of the bubble interface
Latent heat of vaporization
(13)
heat transfer engineering

Figure 5
[18, 19].

Comparison of present experimental data with Eq. (3) of Labuntsov

vol. 31 no. 6 2010